Google already does this themselves. If you search for rare words (e.g. try "indubitably") it will absolutely pull up videos that have the word in the auto-generated transcript and nowhere else (not in descriptions, not in comments).
Also, using "site:youtube.com" on Google works perfectly for me. If I look up "site:youtube.com david letterman" it gives me the David Letterman channel, followed by a seemingly infinite number of Letterman clips. Precisely what I'd expect.
The only thing I can reproduce that you're complaining about is that Google (and YouTube) search don't seem to index YouTube user comments, in contrast to Reddit. But Google doesn't seem to index comments-attached-to-content anywhere on the internet -- not even comments on articles at mainstream publications like the New York Times. Which is probably more of a feature than a bug -- comments on both YouTube videos and news articles tend to be a lot of emotional reactions and repeated opinions which aren't worth searching at all. In contrast, many (not all) Reddit threads are often very informative and the "main content", so it makes sense Google indexes them.
So I don't really see anything to complain about here, from my perspective.
"having a distribution that's both radially symmetric" site:youtube.com
would return 3b1b's "Why π is in the normal distribution" video, which has that in subtitles at 22:28.
Even without the site: term, all I get is an allreadable.com page that's scraped the subtitles for that video. Allreadable appears at first glance to be a site owned by someone in China and hosted on liquidweb.
I just checked and it returns that video as the first result if you put your phrase into the YouTube search box in quotes, so that's good news.
I wonder why YouTube indexes the transcripts for YouTube search, but Google chooses not to include them in its index for Google search? Seems like an intentional decision since it's the same company after all.
Also, using "site:youtube.com" on Google works perfectly for me. If I look up "site:youtube.com david letterman" it gives me the David Letterman channel, followed by a seemingly infinite number of Letterman clips. Precisely what I'd expect.
The only thing I can reproduce that you're complaining about is that Google (and YouTube) search don't seem to index YouTube user comments, in contrast to Reddit. But Google doesn't seem to index comments-attached-to-content anywhere on the internet -- not even comments on articles at mainstream publications like the New York Times. Which is probably more of a feature than a bug -- comments on both YouTube videos and news articles tend to be a lot of emotional reactions and repeated opinions which aren't worth searching at all. In contrast, many (not all) Reddit threads are often very informative and the "main content", so it makes sense Google indexes them.
So I don't really see anything to complain about here, from my perspective.